Enigma 1654: Tricky cards

Shown right are two of the cards Joe asked Penny to make for him. Joe specified four colours (A, B, C and D) and Penny could choose any one of them for any of the four areas.

Penny had only made a few cards when she turned one round and noticed that it was the same as the one she had just made. She had assumed that all the cards must be different, so she set about calculating how many different cards made up a full set.